Draghi, usually quite circumspect in his answers, wondered for a second if he should speak his mind, before confessing:

"We are ... frustrated, yes certainly. We view improvements in the financial markets. We think financial markets are the only and the necessary channel through which monetary policy is transmitted."

For months, the ECB has been hoping its ultra-easy money policy would translate into an improvement for the economy. Draghi said the central bank had been closely "trying to examine reality, to see whether these impulses we transmitted to the economy get translated into better welfare, lower unemployment, better economic activity."

But the ECB's latest loan survey showed lending to nonfinancial firms continued to contract in March, by more than one percent on an annual basis.

Still, Draghi said the ECB was not ready to put more risk on its balance sheet by lending directly to the economy.

"You don't go around with helicopter money, throwing money," he said. "In Europe you go through banks, you don't have capital markets as you have in the U.S., and so we have to go via the banking system."

Draghi also said people urging the ECB to do more should keep in mind its mandate, which is solely to fight inflation, unlike the Federal Reserve's dual mandate on growth and inflation.

The Pope's remarks on Twitter notwithstanding, Draghi's comments were all about the limitations of central bank action.

"Many of the problems that we see today in competitiveness in the labor market, in the tax area, don't have anything to do with monetary policy, neither can they be fixed with monetary policy," he said.

What can solve this then, given the lack of political willpower after a five-year debt crisis? Divine intervention perhaps?